The Spaniard, who does not turn 20 until next month, was in commanding form on Sunday in a 6-3 6-4 victory over the second seed which adds to his 2023 title wins in Buenos Aires and Indian Wells.
Alcaraz remains behind Novak Djokovic in the rankings but, with the Serbian troubled by an elbow problem and out of the Madrid Open, and Rafael Nadal struggling to play on clay at all as he battles a hip injury, the teenager could go into the French Open as the favourite.
Tsitsipas could find no answer to the all-round brilliance of Alcaraz, who missed the start of the season through injury but has been making up for lost time ever since.
After winning his ninth title, Alcaraz said: "It's incredible. To feel this energy and lift the trophy in Barcelona in front of my family and friends, and most members of my team are here as well.Â
"Playing this level and to lift the trophy in front of them is a good feeling for me."
In Banja Luka, Bosnia and Herzegovina, there was an emotional ATP triumph for Serbia's Dusan Lajovic, who followed up his upset of countryman Djokovic in the quarter-finals by taking out Russia's second seed Andrey Rublev 6-3 4-6 6-4.
Rublev, who won the biggest title of his career in Monte Carlo last week, fought back from 5-1 down in the decider but 70th-ranked Lajovic held his nerve to clinch his second ATP title, four years after his first.
Lajovic said: "I am thrilled and overwhelmed that I did it this week. The last time I was in a final was four years ago and I have been through a lot since then."
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